If x and y are distinct positive integers : GMAT Data Sufficiency (DS)
Check GMAT Club Decision Tracker for the Latest School Decision Releases http://gmatclub.com/AppTrack

 It is currently 21 Jan 2017, 20:33

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# If x and y are distinct positive integers

Author Message
TAGS:

### Hide Tags

Manager
Joined: 24 Aug 2012
Posts: 129
Followers: 2

Kudos [?]: 212 [0], given: 2

If x and y are distinct positive integers [#permalink]

### Show Tags

06 Nov 2012, 17:37
1
This post was
BOOKMARKED
00:00

Difficulty:

65% (hard)

Question Stats:

58% (02:32) correct 42% (01:21) wrong based on 149 sessions

### HideShow timer Statistics

If x and y are distinct positive integers, what is the value of x^4 - y^4?

(1) (y^2 + x^2)(y + x)(x - y) = 240
(2) x^y = y^x and x > y
[Reveal] Spoiler: OA

_________________

Push +1 kudos button please, if you like my post

Intern
Status: wants to beat the gmat
Joined: 18 Jul 2012
Posts: 20
Location: United States
Followers: 0

Kudos [?]: 9 [0], given: 1

Re: If x and y are distinct positive integers [#permalink]

### Show Tags

06 Nov 2012, 17:50
1. sufficient b/c doing the algebra, comes out to be x^4 - y^4 = 240.
2. sufficient b/c only case this works is when x = 4 and y = 2
4^2 = 2^4

Math Expert
Joined: 02 Sep 2009
Posts: 36590
Followers: 7092

Kudos [?]: 93374 [0], given: 10557

Re: If x and y are distinct positive integers [#permalink]

### Show Tags

07 Nov 2012, 02:40
If x and y are distinct positive integers, what is the value of x^4 - y^4?

(1) (y^2 + x^2)(y + x)(x - y) = 240 --> $$(x^2 +y^2)(x^2 - y^2) = 240$$ --> $$x^4-y^4= 240$$. Sufficient.

(2) x^y = y^x and x > y. With trial and error we can find that, since x and y are positive integers and x>y, then x=4 and y=2. Sufficient.

_________________
Intern
Status: Studying
Joined: 09 Dec 2012
Posts: 27
Location: Russian Federation
Concentration: Finance, Strategy
GMAT Date: 04-06-2013
GPA: 3.6
WE: Consulting (Insurance)
Followers: 0

Kudos [?]: 30 [0], given: 1

Re: If x and y are distinct positive integers [#permalink]

### Show Tags

27 Apr 2013, 01:04
bunuel

ok, 1 is pretty much understandable, but for 2, how do you get there? what is the mind process here, in similar problems on the actual test, how do you get there in under 2 minutes? do you start just plugging the numbers in?
MBA Section Director
Status: On vacation...
Affiliations: GMAT Club
Joined: 21 Feb 2012
Posts: 3946
Location: India
City: Pune
GMAT 1: 680 Q49 V34
GPA: 3.4
Followers: 396

Kudos [?]: 2887 [0], given: 2161

Re: If x and y are distinct positive integers [#permalink]

### Show Tags

13 Aug 2013, 07:50
lololol650 wrote:
bunuel

ok, 1 is pretty much understandable, but for 2, how do you get there? what is the mind process here, in similar problems on the actual test, how do you get there in under 2 minutes? do you start just plugging the numbers in?

Statement 2 is sufficient because, only one pair of integers that can satisfy the condition $$X^y = Y^x$$ is 4 and 2. $$(4^2 = 2^4)$$. So whenever you see such equation you can rest assured that one integer must be 4 and other one be 2.

Hope that helps.
_________________
Current Student
Joined: 06 Sep 2013
Posts: 2035
Concentration: Finance
GMAT 1: 770 Q0 V
Followers: 62

Kudos [?]: 594 [0], given: 355

Re: If x and y are distinct positive integers [#permalink]

### Show Tags

21 Jan 2014, 06:26
Narenn wrote:
lololol650 wrote:
bunuel

ok, 1 is pretty much understandable, but for 2, how do you get there? what is the mind process here, in similar problems on the actual test, how do you get there in under 2 minutes? do you start just plugging the numbers in?

Statement 2 is sufficient because, only one pair of integers that can satisfy the condition $$X^y = Y^x$$ is 4 and 2. $$(4^2 = 2^4)$$. So whenever you see such equation you can rest assured that one integer must be 4 and other one be 2.

Hope that helps.

Not really, they have to specify that such numbers must be positive integers otherwise one could have 4 combinations of 2 and 4
Re: If x and y are distinct positive integers   [#permalink] 21 Jan 2014, 06:26
Similar topics Replies Last post
Similar
Topics:
3 If x and y are distinct positive integers. . . 5 11 Nov 2016, 04:50
13 x, y, and z are all distinct positive integers 4 27 Mar 2016, 12:36
3 If x and y are distinct positive integers, what is the value of .... 1 10 Sep 2015, 14:00
2 If x and y are two distinct positive integers, is x/y an int 9 18 Aug 2014, 08:00
21 If x and y are distinct positive integers, what is the value 8 18 Jul 2010, 07:11
Display posts from previous: Sort by